Research Article
Fuzzy Adaptive Teaching Learning-Based Optimization for
Solving Unconstrained Numerical Optimization Problems
Fakhrud Din ,
1
Shah Khalid ,
1
Muhammad Fayaz ,
2
Jeonghwan Gwak ,
3,4,5,6
Kamal Z. Zamli ,
7,8
and Wali Khan Mashwani
9
1
Department of Computer Science & IT, University of Malakand, KPK, Pakistan
2
Department of Computer Science, University of Central Asia, Naryn, Kyrgyzstan
3
Department of Software, Korea National University of Transportation, Chungju 27469, Republic of Korea
4
Department of Biomedical Engineering, Korea National University of Transportation, Chungju 27469, Republic of Korea
5
Department of AI Robotics Engineering, Korea National University of Transportation, Chungju 27469, Republic of Korea
6
Department of IT & Energy Convergence (BK21 FOUR), Korea National University of Transportation,
Chungju 27469, Republic of Korea
7
Faculty of Computing, Universiti Malaysia Pahang, 26600 Pekan, Pahang Darul Makmur, Malaysia
8
Faculty of Science and Technology, Universitas Airlangga, C Campus JI. Dr. H. Soekamo, Mulyorejo, Surabaya 60115, Indonesia
9
Institute of Numerical Sciences, Kohat University of Science & Technology, KPK, Pakistan
Correspondence should be addressed to Muhammad Fayaz; muhammad.fayaz@ucentralasia.org and Wali Khan Mashwani;
mashwanigr8@gmail.com
Received 9 August 2021; Revised 26 October 2021; Accepted 14 March 2022; Published 30 April 2022
Academic Editor: Ewa Rak
Copyright © 2022 Fakhrud Din et al. is is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Teaching learning-based optimization is one of the widely accepted metaheuristic algorithms inspired by teaching and learning
within classrooms. It has successfully addressed several real-world optimization problems, but it may still be trapped in local optima
and may suffer from the problem of premature convergence in the case of solving some challenging optimization problems. To
overcome these drawbacks and to achieve an appropriate percentage of exploitation and exploration, this study presents a new
modified teaching learning-based optimization algorithm called the fuzzy adaptive teaching learning-based optimization algorithm.
e proposed fuzzy adaptive teaching learning-based optimization algorithm uses three measures from the search space, namely,
quality measure, diversification measure, and intensification measure. As the 50-50 probabilities for exploitation and exploration in
the basic teaching learning-based optimization algorithm may be counterproductive, the Mamdani-type fuzzy inference system of the
new algorithm takes these measures as a crisp inputs and generates selection as crisp output to choose either exploitation or
exploration based on the current search requirement. is fuzzy-based adaptive selection helps to adequately balance global search or
exploration and local search or exploitation operations during the search process as these operations are intrinsically dynamic. e
performance of the fuzzy adaptive teaching learning-based optimization is evaluated against other metaheuristic algorithms in-
cluding basic teaching learning-based optimization on 23 unconstrained global test functions. Moreover, adaptive teaching learning-
based optimization is used to search for near-optimal values for the four parameters of the COCOMO II model, which are then tested
for validity on a software project of NASA. Analysis and comparison of the obtained results indicate the efficiency and com-
petitiveness of the proposed algorithm in addressing unconstrained continuous optimization tasks.
1. Introduction
Optimization is a process of searching and comparing ac-
ceptable solutions until finding the final best solution among
the available solutions. e optimization process encompasses
specific goals generally known as objective functions, a feasible
search region with all valid solutions, and a search procedure
as an optimization method [1]. A solution can be termed best
or poor based on the objective function. e set of values for
design variables in the objective function constitutes the search
Hindawi
Mathematical Problems in Engineering
Volume 2022, Article ID 2221762, 17 pages
https://doi.org/10.1155/2022/2221762